A city planner is rerouting traffic in order to work on a stretch of road. The equation of the path of the old route can be described as y = two fifthsx − 4. What should the equation of the new route be if it is to be parallel to the old route and will go through point (Q, P)?


y − Q = negative five halves(x − P)

y − Q = two fifths(x − P)

y − P = negative five halves(x − Q)

y − P = two fifths(x − Q)

The table should be completed as follows;

Coordinate   Key feature    Does the coordinate        Justification

                                                  make sense  ___________________

(-7.565, 0)   it is a key feature          yes                     it is a zero (root).

(0, 37)          it is a key feature          yes                     it is the y-intercept.

(6, 46)          it is a key feature          yes                     it is the vertex.

A reasonable constraint for the context in set builder notation is {y|y ∈ R ≤ 46}.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph, with a maximum exponent of two (2).

In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this scenario, the y-intercept of this quadratic function can be calculated as follows;

G(x) = -1/4(x²) + 3x + 37

G(0) = -1/4(0²) + 3(0) + 37

G(0) = 37.

In conclusion, the vertex (maximum point) of this quadratic function is given by the ordered pair (6, 46).

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Answer:

10

Step-by-step explanation:

→ Calculate how many are mint ice cream's

\(\frac{1}{3}\) × \(30\) = 10

→ Calculate how many are chocolate

30 - 10 = 20

\(\frac{1}{2}\) × 20 = 10

→ Now find the vanilla

30 - ( 10 + 10 ) = 10

The magnitude of the x-component of this vector is 9.05m.

The angle of inclination of the vector is calculated as;

θ = 90 ⁰ - 48.4 ⁰

θ = 41.6 ⁰

The magnitude of the x-component of the vector is calculated as;

Vx = 12.1 m x cos ( 41.6 )

Vx = 9.05 m

A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.

Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.

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Complete Question:-

Step-by-step explanation:

Solution,

P={2,3,4}

P={x:x ∈ N between 1 and 5}

Q={1,5}

Q={x:x ∈ factors of 5}

I hope you were asking for the same answer .

I hope it helped U

stay safe stay happy

Therefore, the insect population will remain stable, neither increasing nor decreasing and the estimated  stable population is 2.

Given the equation:3-12+16 PO) 15-2+1

In order to determine the stability of a population of insects, we must first calculate the equilibrium value of PO.

A population's equilibrium is defined as the point at which the population remains stable over time, indicating that the population is neither declining nor growing indefinitely.

Stable population equilibrium is defined as follows:

Let P* be the equilibrium value of the population.

This implies that:P* = 15 - 2 + 1 / 3 - 12 + 16

This simplifies to:P* = 14/7 or 2

Therefore, the equilibrium value of the insect population is 2. If the population is greater than 2, it will decrease. If it is less than 2, it will increase.

In this case, the population of insects will settle into an equilibrium state.

The value of the stable population is 2.

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Answer:

Ecuación estándar de un círculo

(x−2)2+(y−2)2=25

Forma general de la ecuación de un círculo

x2−4x+y2−4y−17=0

Ecuaciones paramétricas de un círculo

x=5cosθ+2y=5sinθ+2

Step-by-step explanation:

Ecuación Estándar de un Círculo

La ecuación estándar de un círculo con el centro en (x_0, y_0) y radio r es

(x^2-x_0) + (y^2-y_0)=r^2

Ecuaciones Paramétricas de un Círculo

Las ecuaciones paramétricas de un círculo con el centro en (x_0, y_0) y radio r son

x=r cos \theta + x_0\\y=r sin \theta + y_0

Ecuación General de un Círculo

La ecuación general de un círculo con el centro en (x_0, y_0) y radio r es

x^2+ax+y^2+by+c=0,

donde

a=-2x_0\\b=-2y_0\\c=x^2_0+y^2_0-r^2

The values stored in the list numlist are [0, 2, 4, 6, 8].

The list "numlist" is an array with 10 elements. The values stored in the list depend on the values of "i" as the for loop iterates from 0 to 9.

The "if" statement inside the loop checks if the value of "i" is even using the % operator which returns remainder, and if it is, the value of "i" is stored in the "numlist" at the corresponding index. Therefore, the values stored in the "numlist" would be 0, 2, 4, 6, 8, and the other elements would be left uninitialized.

--The question is incomplete, answering to the question below--

"what values are stored in the list numlist?

numberList() {

  for(i = 0; i < 10; i++) {

      if( i % 2 == 0) {

         numlist[i] = i

         }

    }

}"

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Answer:

3

Step-by-step explanation:

as u add 2 + 1 from the 6 and 7 hours

Answer:

58000 x 15= 87000

Step-by-step explanation:

you just have to multiply it by 15

Answer:

667000

Step-by-step explanation:

Have to find what 15% of 580000 is first:

580000 x 0.15 (15% as decimal --> divide by 100) = 87000

Next add what 15% of 580000 is to 580000:

580000  + 87000 = 667000

The test used to determine whether or not first-order autocorrelation is present is the Durbin-Watson test.

1. Fit a regression model to the data.

2. Obtain the residuals, which represent the differences between the observed values and the predicted values from the regression model.

3. Calculate the Durbin-Watson statistic, which is a ratio of the sum of squared differences between adjacent residuals to the sum of squared residuals.

4. Compare the calculated Durbin-Watson statistic to critical values from a Durbin-Watson table or use statistical software to determine if there is significant autocorrelation.

5. The Durbin-Watson statistic ranges from 0 to 4, where a value around 2 suggests no autocorrelation, a value below 2 indicates positive autocorrelation, and a value above 2 indicates negative autocorrelation.

6. By analyzing the Durbin-Watson statistic, researchers can make conclusions about the presence or absence of first-order autocorrelation in the regression model.

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Answer:

x = 55

Step-by-step explanation:

Given that x varies inversely as y then the equation relating them is

x = \(\frac{k}{y}\) ← k is the constant of variation

To find k use the condition x = 11 when y = 15

11= \(\frac{k}{15}\) ( multiply both sides by 15 )

165 = k

x = \(\frac{165}{y}\) ← equation of variation

When y = 3 , then

x = \(\frac{165}{3}\) = 55

To find the power series representation for the function f(x) = 1 + x^8, we can expand it as a Taylor series centered at x = 0. We have: f(x) = 1 + x^8

To find the power series representation, we'll express it in terms of the variable t, where t = x^8:

f(x) = 1 + t

Now, we can rewrite the function in terms of the variable t and find its power series representation:

f(x) = 1 + t = 1 + x^8

The power series representation centered at x = 0 is:

f(x) = 1 + x^8 = 1 + (x^8)(1) = 1 + x^8

The interval of convergence for this power series representation is given by the condition |x| < √(R), where R is the radius of convergence. In this case, since the power series only consists of a single term, the interval of convergence is the set of all real numbers (-∞, +∞).

Similarly, for the function f(x) = 1 + x^25, we can find its power series representation centered at x = 0:

f(x) = 1 + x^25

Again, expressing it in terms of the variable t where t = x^25:

f(x) = 1 + t

The power series representation centered at x = 0 is:

f(x) = 1 + x^25 = 1 + (x^25)(1) = 1 + x^25

The interval of convergence for this power series representation is also (-∞, +∞) since it consists of a single term.

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Answer:

$1.00

Step-by-step explanation:

Dimes = 10 / Nickels = 5 / Quarters = 25

6(10) + 3(5) + 1(25)

60 + 15 + 25 = 100 so that makes it $1.00

The concave mirror should be placed at a distance of 2r from the wall to form a real image of the object on the wall. The magnification of the image is expressed using three significant figures is -0.500.

if the object is placed at a distance r in front of a concave mirror whose radius of curvature is also r, then the image is formed at the same distance r behind the mirror. This is a special case called the "center of curvature" configuration.

To form a real image on the wall, the mirror must be placed such that the object is beyond the mirror's focal point. The focal length of the mirror is half of its radius of curvature, so the focal length is f = r/2.

If the object is placed at a distance x from the mirror, then using the mirror equation:

1/f = 1/do + 1/di

where do is the distance of the object from the mirror and di is the distance of the image from the mirror. In this case, do = x and di = r, so we get:

1/r = 1/x - 1/f

Substituting f = r/2, we get:

1/r = 1/x - 2/r

Solving for x, we get:

x = 2r

Therefore, the mirror should be placed at a distance of 2r from the object to form a real image on the wall.

To find the magnification of the image, we use the magnification equation:

m = -di/do

where m is the magnification, di is the distance of the image from the mirror, and do is the distance of the object from the mirror. In this case, do = x = 2r and di = r, so we get:

m = -r/(2r) = -1/2

Therefore, the magnification of the image is -0.500.

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An equation that models the parabola formed when a cross-section is taken through the reflector’s central axis is y= 1/12(x-0)^2+0

This answer works as an upward parabola

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. One way to describe a parabola is with a point and a line.

The formula for a vertical parabola is y=1/4p(x-h)^2+k

In this problem, it is given that the vertex is at the origin (0,0) and the focus (the bulb), is 3 centimeters away from the vertex.

Now, you know the values of the variables. Fill in the values

FROM THE FORMULA:

1/4p turns into 1/12 since p is 3.

(x-h)^2+k turns into (x-0)^2+0, since h and k were the values of the vertex which was 0,0

once all the variables are given values (except x and y) you have made your equation!

The answer is y=1/12(x-0)^2+0

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Answer:

uhm chile anyways

Step-by-step explanation:

i just want points lol

Given statement solution is :-Time cannot be negative in this context, we discard the solution t = -1,  the book will hit the ground after approximately 2.5 seconds.

To find the time when the book hits the ground, we need to determine when the height (h) becomes zero. We can set up the equation and solve for t.

The equation given is:

h = -\(16t^2 + 24t + 40\)

Setting h = 0, we have:

0 = \(-16t^2 + 24t + 40\)

Now we can solve this quadratic equation. There are a few methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula. In this case, we'll use the quadratic formula:

t = \((-b ± √(b^2 - 4ac)) / (2a)\)

For our equation, a = -16, b = 24, and c = 40. Plugging these values into the quadratic formula, we get:

t = \((-24 ± √(24^2 - 4*(-16)40)) / (2(-16))\)

t = \((-24 ± √(576 + 2560)) / (-32)\)

t = (-24 ± √3136) / (-32)

t = (-24 ± 56) / (-32)

Now we have two possible solutions:

t = (-24 + 56) / (-32) = 32 / (-32) = -1

t = (-24 - 56) / (-32) = -80 / (-32) = 2.5

Since time cannot be negative in this context, we discard the solution t = -1. Therefore, the book will hit the ground after approximately 2.5 seconds.

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Given:

A rectangular lot measures 160 m by 240 m.

To find:

The area in hectare​.

Solution:

We know that, the area of a rectangle is

\(Area=Length\times width\)

Using this formula the area of the rectangular lot measures 160 m by 240 m is

\(Area=160\times 240\)

\(Area=38400\)

Therefore, the area of the rectangular lot is 38400 square units.

Answer:

C. y = 2 (x + 3)³ − 4

Step-by-step explanation:

y = x³

Stretch vertically by 2.

y = 2x³

Shift horizontally 3 units to the left.

y = 2 (x + 3)³

Shift vertically 4 units down.

y = 2 (x + 3)³ − 4

Answer:

29

Step-by-step explanation:

this sequence is an arthimetic sequence in which every second number is 8 more than the previous number.so the next number is 21+8=29

The eight number is 45

Let x represent the unknown number

The mean is 47

The seven numbers are

50,27,45,72,67,32 and 38

The eight number can be calculated as follows

50 + 27 + 45 + 72 + 67 + 32 + 38 + x/8= 47

cross multiply both sides

331 + x/8= 47

331 + x= 47× 8

331 + x= 376

x= 376-331

x= 45

Hence the eight number is 45

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The  transformation of \(\(y= \frac{x^{4} }{6x+6}\)\) graph is compressed by a factor of 2.

The function is a rational function in which the numerator is a degree 4 polynomial, and the denominator is a degree 1 polynomial.

Rational functions are in the form of \(\(f(x) = \frac{p(x)}{q(x)}\)\), where p(x) and q(x) are polynomial functions and the degree of p(x) is less than the degree of q(x).

To transform a graph of a function, one can translate, stretch, or reflect it.

Here are some of the transformations of the function \(\(y= \frac{x^{4} }{6x+6}\)\)

Vertical Shift: To get the new graph, we add or subtract a constant from the function.

When f(x) is replaced with f(x) + k, we get a graph that is k units above the graph of f(x). In this case, if we subtract 2 from the equation, we get the following equation:

\(y = (x^4) / (6x+6) - 2\)

This means that the graph of the function is shifted 2 units downwards.

Horizontal Shift: To get the new graph, we add or subtract a constant to the variable.

When f(x+c) is replaced with f(x), the graph is shifted c units to the left.

When f(x-c) is replaced with f(x), the graph is shifted c units to the right.

In this case, we can shift the graph by substituting x-2 for x in the function.

The new function is: \(y = ((x-2)^4) / (6(x-2)+6)\)

This means that the graph is shifted 2 units to the right.

Vertical Stretch/Compression: When a constant is multiplied to the function, the graph is vertically stretched or compressed.

In this case, if the function is multiplied by 2, we get the following function:

\(y = 2(x^4) / (6x+6)\)

This means that the graph is compressed by a factor of 2.

It can also be stretched by dividing the function by a constant.

Horizontal Stretch/Compression:

When a constant is multiplied to the variable of the function, the graph is horizontally stretched or compressed. In this case, if the variable is divided by 2, we get the following function:

\(y = (x^4) / (3x+3)\)

This means that the graph is compressed by a factor of 2.

It can also be stretched by multiplying the variable by a constant.

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Answer:

(2,14)

Step-by-step explanation:

so i solved this with substitution but there are other methods to solve this!

equation 1 : y = -x + 16
equation 2 : y = x + 12

solve for y in equation 1 !!
y = -x + 16
(add x on both sides)
y + x = 16
(subtract y on both sides)
x = -y + 16

equation 1 now equals : x = -y + 16

substitute equation 1 into equation 2 :)

y = (-y + 16) + 12
(add 16 + 12)
y = -y + 28
(add y on both sides)

2y = 28
(divide 2 on both sides)
y = 14

now to solve for x you can insert y !
you can use equation 1 or equation 2 to solve for x.

i'm using equation 2 :
y = x + 12
(14) = x + 12
(subtract 12 on both sides)
x = 2

therefore, the answer is (2, 14).

hope this helps :p

The cash flow to stockholders for 1998 is -$4 million.

To calculate the cash flow to stockholders for 1998, follow these steps:

Identify the dividends paid: Brandy's Candies paid $23 million in dividends during 1998.

Determine the net common stock repurchases: Brandy's Candies made net common stock repurchases of $27 million during 1998.

Subtract the net common stock repurchases from the dividends paid: $23 million - $27 million = -$4 million.

The resulting cash flow to stockholders for 1998 is -$4 million, indicating a net outflow of cash from stockholders.

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x= 4  is a number and five is at least half the difference of six and the same number.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.

Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.

Recognizing the units and values is crucial when using the unitary technique to a problem.

Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.

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The fractional scale for a map where 1 cm represents 1 km on Earth would be written as 1:100,000. This means that one unit of measurement on the map (1 cm) represents 100,000 units of measurement in the real world (1 km).

A fractional scale on a map represents the relationship between distances on the map and the corresponding distances on the Earth's surface. In this case, where 1 cm on the map represents 1 km on Earth, the fractional scale is determined by comparing the two distances.

The numerator of the fraction represents the map distance (1 cm), and the denominator represents the equivalent Earth distance (1 km). To convert the numerator and denominator into the same units, both are typically expressed in the same unit of measurement, such as centimeters or kilometers. Therefore, the fractional scale for this scenario would be written as 1:100,000, indicating that one unit of measurement on the map corresponds to 100,000 units of measurement on Earth.

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The stored energy during the stride when the stretch causes the center of mass to lower by 10 mm is approximately 6.038 Joules.

The stored energy can be determined from the height change and the mass of the person.

The formula for potential energy is as follows: PE = mgh

Where:PE = Potential energy (Joules)

m = Mass (kg)

g = Acceleration due to gravity (9.8 m/s^2)

h = Height (m)

First, convert the 10mm to meters:

10 mm = 0.01 meters

Then, substitute the given values:

PE = (61 kg)(9.8 m/s^2)(0.01 m)

PE = 6.018 J

Therefore, the stored energy is 6.018 Joules.

To calculate the stored energy during a stride when the stretch causes the center of mass to lower by 10 mm, we can use the gravitational potential energy formula.

The gravitational potential energy (U) is given by the equation:

U = mgh

Where:

m = mass of the object (in this case, the person) = 61 kg

g = acceleration due to gravity = 9.8 m/s²

h = change in height = 10 mm = 0.01 m

Substituting the given values into the equation, we have:

U = (61 kg) * (9.8 m/s²) * (0.01 m)

U = 6.038 J

Therefore, the stored energy during the stride when the stretch causes the center of mass to lower by 10 mm is approximately 6.038 Joules.

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Answer:

a,g,e

Step-by-step explanation:

Answer:

58

Step-by-step explanation:

You just have to replace the value of n with 4.

C(n) = 46 + 3n

C(4) = 46 + 3(4)

       = 46 + 12

       = 58